Final answer:
The fastest downward motion of an elevator, with the up direction considered positive, is free fall, since the elevator accelerates at the maximum rate of gravity without any other forces acting on it. Thus, option d is correct.
Step-by-step explanation:
When discussing the fastest downward motion for an elevator with the up direction considered positive, we need to analyze the given options. Acceleration can be in any direction, so simply stating 'acceleration' does not specify a downward motion. Deceleration implies a decrease in velocity, which could mean the elevator is slowing down in its downward motion, not necessarily going the fastest. A negative velocity means the elevator is moving downward, but the speed at which the elevator is moving down is not indicated by velocity alone.
Finally, free fall describes a motion where gravity is the only force acting on the elevator, and it is accelerating downward at g (9.80 m/s2), which would typically be the fastest downward motion in the absence of air resistance or other forces.
Accordingly, free fall represents the situation where the elevator would be moving the fastest in downward motion since it would be accelerating at the maximum rate due solely to gravity.